相关论文: Stabilizing unstable periodic orbits in the Lorenz…
An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the…
The double Hamiltonian Hopf bifurcation is studied, i.e. a generic two-parametric unfolding of a smooth Hamiltonian system with four degrees of freedom which has at the critical value of parameters the equilibrium with two pairs of double…
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
Many physical systems exhibit limit cycle oscillations induced by Hopf bifurcations. In aerospace engineering, limit cycle oscillations arise from undesirable Hopf bifurcation phenomena such as aeroelastic flutter and transonic buffet. In…
We investigate a diffusive predator-prey model by incorporating the fear effect into prey population, since the fear of predators could visibly reduce the reproduction of prey. By introducing the mature delay as bifurcation parameter, we…
In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…
Equivariant Pyragas control is a delayed feedback method that aims to stabilize spatio-temporal patterns in systems with symmetries. In this article, we apply equivariant Pyragas control to discrete waves, which are periodic solutions that…
We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control…
Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays.…
This paper aims at completing an earlier work of Russell and Zhang to study internal control problems for the distributed parameter system described by the Korteweg-de Vries equation on a periodic domain T^1. In their article, Russell and…
In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…
In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid film…
Steady states of the Swift--Hohenberg equation are studied. For the associated four--dimensional ODE we prove that on the energy level $E=0$ two smooth branches of even periodic solutions are created through the saddle-node bifurcation. We…
In this paper we analyze a simple mathematical model which describes the interaction between the proteins p53 and Mdm2. For the stationary state we discuss the local stability and the existence of the Hopf bifurcation. Choosing the delay as…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic…
This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie…
In this paper, we derive the algorithm for calculating the normal form of the double Hopf bifurcation that appears in a memory-based diffusion system via taking memory-based diffusion coefficient and the memory delay as the perturbation…